Ukrainian mathematician Marina Vyazovskiy found a solution to the problem of stacking the balls in Euclidean space, on which scientists have worked for centuries.
This became known after the publication of several scientific articles in mid-March, according to bit.ua with reference to Quanta Magazine. Vyazovskiy conducted a study to spaces of dimensions 8 and 24 (the latter in cooperation with other mathematicians).
Scientists are studying the packing of the balls from 1611. German mathematics Johannes Kepler conjectured that the most dense packing of equal sized balls in space is a pyramidal arrangement of oranges in the stores. Despite the simplicity of this task, the solution appeared only in 1998, when American Thomas Hales proved the Kepler conjecture in three dimensions using mathematical arguments and calculations of complex machine.
To visualize the packing of balls in a multidimensional space is difficult, but it is of great practical importance. This task is related to codes of detection and correction of errors in mobile phones, the Internet and space exploration to send messages through the channel with noise.
«Packing balloons in high dimensional spaces is used to improve signal transmission. For example, the code that is associated with the 24-dimensional packing uses the spacecraft Voyager. The signal sent to them to inform about space discoveries, of course, distorted. It is broken down into 24 parts — say, 24 bits. For example, one of them is changing. How to decrypt the signal? Due to the fact that the balls in the package are far from each other to understand what signal wrong, and correct it,» explained the practical significance of his discovery Vyazovskiy, reports Focus.
In his study of the Ukrainian scientists have proved that the best way of packing of balls in Euclidean space of dimension 8 was the E8 lattice and 24 is the Leech lattice. They became the point of intersection of different mathematical areas of number theory, combinatorics, hyperbolic geometry, and physics and string theory. However, to determine the exact reasons for such results of mathematics can not yet.
March 14, Vyazovskiy published scientific article, which has identified a missing feature for the space 8 dimensions. She used the theory of modular forms and 23 pages proved that for this measure is the most optimal lattice E8. A week later appeared another work co-authored with Peter Carnicom, Henry Cohn and three other mathematicians, in which scientists have written about the Leech lattice. Vyazovskiy previously worked on this problem with two Ukrainian mathematicians Andrei Bondarenko and Daniel Radchenko, who then moved on to other projects.
Vyazovskiy Marina grew up in Kiev, studied at the Kiev Lyceum №145, and the mechanical-mathematical faculty of the Kiev national University of Taras Shevchenko. In may 2010 he defended his thesis at the Institute of mathematics of NAS of Ukraine on the theme «Inequalities for polynomials and rational functions and quadrature formulas on the sphere». In 2013 he received his doctorate (Dr. rer. Nat.) at the University of Bonn. Now working in Berlin’s Humboldt University.
About its opening recently wrote for The Huffington Post and Der Spiegel.
We will remind, in 2014 the fields medal (Fields Medal), the most prestigious award in mathematics, was first given by a woman Professor at Stanford University, USA Iranian-born Maryam Mirzakhani.
A Ukrainian woman is that math problem over which scientists have been puzzling for several centuries 06.04.2016